Related papers: Characterization for stability in planar conductiv…
We propose an abstract approach to prove local uniqueness and conditional H\"older stability to non-linear inverse problems by linearization. The main condition is that, in addition to the injectivity of the linearization $A$, we need a…
We introduce the notion of a logarithmic stable map from a minimal log prestable curve to a log twisted semi-stable variety of form $xy=0$. We study the compactification of the moduli spaces of such maps and provide a perfect obstruction…
We consider second-order elliptic equations with oblique derivative boundary conditions, defined on a family of bounded domains in $\mathbb{C}$ that depend smoothly on a real parameter $\lambda \in [0,1]$. We derive sharp regularity…
In this paper we study the inverse conductivity problem with partial data in dimension $n\geq 3$. We derive stability estimates for this inverse problem if the conductivity has $C^{1,\sigma}(\bar\Omega)\cap H^{3/2+\sigma}(\Omega)$…
This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or…
We consider the isoperimetric problem in $\mathbb R^n$ with density for the planar case $n=2$. We show that, if the density is ${\rm C}^{0,\alpha}$, then the boundary of any isoperimetric is of class ${\rm C}^{1,\frac \alpha{3-2\alpha}}$.…
An inverse problem to identify unknown coefficients of a partial differential equation by a single interior measurement is considered. The equation considered in this paper is a strongly elliptic second order scalar equation which can have…
We consider the problem of determining a polyhedral conductivity inclusion embedded in a homogeneous isotropic medium from boundary measurements. We prove global Lipschitz stability for the polyhedral inclusion from the local…
This paper introduces results for characteristically near vector fields that are stable or non-stable in the polar complex plane $\mathbb{C}$. All characteristic vectors (aka eigenvectors) emanate from the same fixed point in $\mathbb{C}$,…
Phase retrieval is concerned with recovering a function $f$ from the absolute value of its Fourier transform $|\widehat{f}|$. We study the stability properties of this problem in Lebesgue spaces. Our main results shows that $$ \|…
We obtain conditions for the differentiability of weak solutions for a second-order uniformly elliptic equation in divergence form with a homogeneous co-normal boundary condition. The modulus of continuity for the coefficients is assumed to…
In this paper we prove stable determination of an inverse boundary value problem associated to a magnetic Schr\"odinger operator assuming that the magnetic and electric potentials are essentially bounded and the magnetic potentials admit a…
This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…
We consider an inverse problem of recovering all spatial dependent coefficients in the time dependent Schr\"odinger equation defined on an open bounded domain in $\mathbb{R}^n$, $n\geq 2$, with smooth enough boundary. We show that by…
This paper studies the polynomial stabilization of an elastic plate with dynamical boundary conditions on a non-smooth domain. To deal with the possible loss of solution regularity induced by boundary singularities, we formulate the problem…
We present a simple proof of the $C^1$ regularity of $p$-anisotropic functions in the plane for $2\leq p<\infty$. We achieve a logarithmic modulus of continuity for the derivatives. The monotonicity (in the sense of Lebesgue) of the…
A novel computational, non-iterative and noise-robust reconstruction method is introduced for the planar anisotropic inverse conductivity problem. The method is based on bypassing the unstable step of the reconstruction of the values of the…
A general shape identification inverse problem is studied in a Bayesian framework. This problem requires the determination of the unknown shape of a domain in the Euclidean space from finite-dimensional observation data with some Gaussian…
We prove stable versions of trace theorems on the sphere in $L^2$ with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into $L^q$ for $q > 2$, by…
In this paper we show that the shear modulus $\mu$ of an isotropic elastic body can be stably recovered by the knowledge of one single displacement field whose boundary data can be assigned independently of the unknown elasticity tensor.